# Inductor/Electromagnet used to lift up a magnet? Joules to Newtons or Joules to Gauss?

With interest in using an electromagnet to lift up a magnet.

I dove in. I will state general information. The set up is unknown but I'm interested in the physics/electrical engineering involved in calculating the amount of ______ needed to lift up a mass (magnet with magnetic strength x).

I reviewed "electromagnets". I see an inductor produces a magnetic field, a summation of the contributions of electrons and we get some equations.

Regarding inductors, Energy is .5LI². We can adjust the power/energy/magnetic flux in an inductor by varying the voltage/current/turns, etc.

Also since V = dϕ/dt, maybe we can integrate velocity to find the magnetic flux or something but idk if magnetic flux is relevant to lifting a magnet on the ground.

So I found a link to the an equation expressing the force between two magnets in Newtons homework and exercises - calculate force between two magnets - Physics Stack Exchange

I see magnetic force is measured in Gauss.

I've nearly finished relearning Classical Mechanics, so I'm thinking about using F = ma, and I'm not sure how the inductor/"electromagnet" ties into this nicely.

I don't know how to convert an inductors properties into Gauss, nor express it as a function of distance, and I think you guys can help!

I considered using F = kqq/R or some other attraction law, but still idk how to relate an inductor and it's Joules or other properties to "magnetic strength" I can use in a kinematics analysis.

• do you have a question? Feb 3, 2021 at 3:12
• @jsotola I’m hoping someone can help me move forward in this analysis by providing relevant information, which may lead me to better questions and/or understanding, and/or finding a solution. In other words, there are gaps in where I want to be and what I know so I’m hoping people can fill in the holes. Feb 3, 2021 at 3:14
• @RenzoM-Svartz Edit your question to improve it as people ask for clarification. You also have to ask an actual question, preferably phrased as one, with a question mark. It sounds like you want to know how to calculate the strength of an electromagnet, calculate its field strength in gauss, and also convert the field strength of some other known magnet to gauss so you can use your equation on them? Perhaps I can interest you in a Finite Element Magnetic Modeller(FEMM) tool sir? It's the sane person's alternative to hand calculating the properties of magnetics.
– K H
Feb 3, 2021 at 3:26
• That said maybe someone can get you partway there if you nicen your question up a bit, although parts of this smell like physics SE to me.
– K H
Feb 3, 2021 at 3:27
• @KH Excuse me friend. I tried my best to write this post/seeking help without knowing what I’m looking for. And thank you, I’d like to hear about that. I just started learning how to use COMSOL Multiphysics (just finished the tutorial series) and I think these software are similar! Feb 3, 2021 at 3:29

Your description revolves around magnets and mechanical force which makes the term co-energy very relevant. I'm sure you can find plenty of information regarding that.

Here is a small example on how magnetic force could be calculated. You have a coil with core as well as an object with relatively high permeability $$\\mu_r\$$. Then the air gaps are the main magnetic resistances in the magnetic circuit.

The magnetic resistance of both air gaps is: $$R_L = \frac{2 d}{A_L \mu_0}$$

The magnetomotive force for $$\N\$$ turns of the coil is: $$\theta_0 = Ni$$

You can then calculate the magnetic co-energy: $$E_c(i,d) = \frac{1}{2}\psi i = \frac{1}{2}\phi \theta_0 = \frac{\theta_0 ^2}{2 R_{L}} = \frac{N^2 i^2 A_{L} \mu_0}{4 d}$$

From the co-energy, the force can be calculated using partial derivative regarding the distance $$\d\$$: $$F(i,d) = \frac{\partial E_c}{\partial d} = -\frac{N^2 i^2 A_{L} \mu_0}{4 d^2}$$ Source: Lecture Notes: Mechatronics and Electrical Drives

You should be able to use this as a starting point for more complex arrangements. If you are not familiar with magnetic circuits, that might also be worth researching.